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Lévy's constant

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(Redirected from Khinchin-Lévy constant)

In mathematics Lévy's constant (sometimes known as the Khinchin-Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions. In 1936 French mathematician Paul Lévy showed that the denominators q_n of the convergents of the continued fraction expansions of almost all real numbers satisfy

$\lim_{n \to \infty}{q_n}^{1/n}=e^{\pi^2/(12\ln2)}\approx 3.2758229$

Lévy's constant is the constant on the right hand side of this expression, and is approximately equal to 3.275 822 918 7... The term is also sometimes used to refer to the logarithm of the right hand side of this expression, which is approximately equal to 1.186 569 110 4...

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